In conventional techniques for using digitized data samples to determine fundamental power system frequency phasors, a small time-varying error is produced by mismatch between the actual power system frequency and the nominal power system frequency (the sampling frequency divided by the number of samples per cycle). In situations wherein high accuracy is not needed, the error is typically not corrected. However, the error does interfere with sensitive measurements and calculations of negative sequence quantities and differential quantities, for example.
Estimating power system voltages and currents when data windows are uneven due to slowly varying frequency, slowly varying spacing of data points, or variable size can be especially challenging. Conventional methods for calculating power system voltage and current phasors generally assume that data samples are substantially evenly spaced in time and do not include efficient techniques for estimating noise and measurement uncertainty. Although assumptions about even spacing are adequate for many applications, some applications have data points that are not evenly spaced. For example, a motor driven by an electronic control has a power frequency which can vary rapidly. Some controls use a concept referred to as "space vector control" in which the phase angles of applied voltages are controlled directly and may change rapidly in a non-uniform sequence of phase angles. In these controls, raw data points used to estimate fundamental voltage and current phasors are, in effect, spaced unevenly over the sinusoidal function on which they are based.
Phadke et al., Computer Relaying for Power Systems, Research Studies Press, 1988, describes a noise and uncertainty estimator, referred to as a transient monitor, which uses the sum of the absolute values of the errors and requires a number of multiplication steps which is proportional to the square of the number of samples in the data window.
Commonly assigned Koegl et al., U.S. Pat. No. 5,514,978, describes a method for detecting stator turn faults that is particularly useful in AC motors energized directly from power lines. The method of Koegl et al. is based on an assumption of approximately evenly spaced samples of voltage and current with only slight frequency variations and has limitations with respect to motors that are energized by variable frequency voltages or that experience rapid changes in power system frequency. In Koegl et al., U.S. Pat. No. 5,514,978, sensitive measurements of negative sequence current are used to detect stator turn to turn faults. Values are calculated using raw samples of voltages and current, phasors are corrected for slight variations in power system frequency, and positive and negative sequence currents are then calculated using the phasors.
As described in commonly assigned Premerlani et al, U.S. application Ser. No. 08/617,718, "Self Tuning and Compensating Turn Fault Detector," filed Apr. 1, 1996, sensitivity can be increased through an adaptive learning process to obtain the residual negative sequence current as a function of load and voltage. The fault current is obtained after all sources of negative sequence current are determined and subtracted from the measured negative sequence current. To correct phasors due to variations in motor excitation frequency, the drift in the power system frequency was measured and a corrective algorithm was applied. In the situation of a variable speed drive, if the applied frequency is changing rapidly, the corrective algorithm does not provide as much accuracy as would be desirable.
High speed detection of faults on multi-terminal power system transmission lines is needed in situations where data transmitted digitally between pairs of terminals in a system is partially lost. Commonly assigned Adamiak et al., U.S. application Ser. No. 08/713,295, "Digital Current Differential System," filed Sep. 13, 1996, describes a multi-terminal system wherein fundamental power system frequency voltages and currents are calculated from digitized samples of voltages and currents with a data window which can have variable sizes for use in digital devices that measure fundamental frequency voltage or current components. The "phaselet" technique partitions the calculation into two processes. The first process is a calculation of partial sums of the data samples multiplied by one cycle weights. The second process is a summation of the partial sums over the width of the desired data window and a correction for distortion caused by the one cycle weights. Occasional failures of the digital channel that result in lost information were addressed by resetting the computation window after data again became available. A slight delay in fault detection can occur in the event that some phaselet data is lost at the beginning of a fault.